Several aspects of the evolution of star-forming galaxies are studied using measures of the two-dimensional surface brightness profiles extracted from Hubble Space Telescope images of a sample of 341 faint objects selected from the CFRS and LDSS redshift surveys. The galaxies have 0 < z < 1.3. The size function of disk scale lengths in disk-dominated galaxies (i.e., with bulge-to-total ratios, B/T ≤ 0.5) is found to stay roughly constant to z ∼ 1, at least for those larger disks with exponential scale lengths α-1 > 3.2 h50-1 kpc, where the sample is most complete and where the disk and bulge decompositions are most reliable. This result, which is strengthened by inclusion of the local de Jong et al. size function, suggests that the scale lengths of typical disks cannot have grown substantially with cosmic epoch since z ∼ 1, unless a corresponding number of large disks have been destroyed through merging. In addition to a roughly constant number density, the galaxies with large disks, α-1 ≥ 4 h50-1 kpc, have, as a set, properties consistent with the idea that they are similar galaxies observed at different cosmic epochs. However, on average, they show higher B-band disk surface brightnesses, bluer overall (U- V) colors, higher [O II] λ3727 equivalent widths, and less regular morphologies at high redshift than at low redshift, suggesting an increase in the star formation rate by a factor of about 3 to z ∼ 0.7. This is consistent with the expectations of recent models for the evolution of the disk of the Milky Way Galaxy. The evolution of the large disk galaxies with scale lengths α-1 ≥ 4 h50-1 kpc, is probably not sufficient to account for the evolution of the overall luminosity function of galaxies over the interval 0 < z < 1, especially if Ω ∼ 1. Analysis of the half-light radii of all the galaxies in the sample and construction of the bivariate size-luminosity function suggests that larger changes in the galaxy population are due to smaller galaxies, those with half-light radii around 5 h50-1 kpc (i.e., disk scale lengths of 3 h50-1 kpc or less).